Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem
Affine matrix rank minimization problem is a famous problem with a wide range of application backgrounds. This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a sm...
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| Veröffentlicht in: | Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-14 |
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| creator | Cui, Angang Sun, Kai Peng, Jigen Zhao, Fujun |
| description | Affine matrix rank minimization problem is a famous problem with a wide range of application backgrounds. This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a small number of linear measurements. Characterized via restricted isometry constant, we elaborate the theoretical guarantees in both noise-free and noisy cases. Two thresholding operators are discussed and numerical demonstrations show that FBRT algorithms have better performances than some state-of-the-art methods. Particularly, the running time of FBRT algorithms is much faster than the commonly singular value thresholding algorithms. |
| doi_str_mv | 10.1155/2020/9578168 |
| format | Article |
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This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a small number of linear measurements. Characterized via restricted isometry constant, we elaborate the theoretical guarantees in both noise-free and noisy cases. Two thresholding operators are discussed and numerical demonstrations show that FBRT algorithms have better performances than some state-of-the-art methods. 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| ispartof | Mathematical problems in engineering, 2020, Vol.2020 (2020), p.1-14 |
| issn | 1024-123X 1563-5147 |
| language | eng |
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| source | Wiley Online Library Open Access; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Algorithms Combinatorial analysis Fines & penalties Mathematical analysis Matrix methods Noise Optimization Recovery |
| title | Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem |
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